Tips for replacing Larson storm door screen with pet proof one, without bowing the screen frame?

I just installed this Larson storm door, and it comes with interchangeable glass and screen. I'm wanting to replace the screen with a pet resistant screen, I have multiple cats and they're all trouble makers who would destroy a regular screen instantly... I just swapped the screen out, and ended up with a warped frame, leaving me unable to attach the newly replaced screen frame to the door. Anyone have tips for preventing the frame from warping when installing the new screen? It's roughly 28"x72", and I've never replaced a screen before